b^2-6b-121=-9

Solution for b^2-6b-121=-9 equation:

b^2-6b-121=-9

We move all terms to the left:

b^2-6b-121-(-9)=0

We add all the numbers together, and all the variables

b^2-6b-112=0

a = 1; b = -6; c = -112;
Δ = b2-4ac
Δ = -62-4·1·(-112)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-22}{2*1}=\frac{-16}{2}
=-8
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+22}{2*1}=\frac{28}{2}
=14
$